The Florida Fish and Wildlife Conversation Commission (FWC) plans to hire hunters to kill the Burmese python, an invasive species in Everglades, South Florida. It is estimated that there are 100,000 pythons in Everglades and their population is governed by P' = P(100,000 – P). Assume that each hunter kills 5 python everyday. At least how many hunters should FWOC hire in order to completely remove the python from the area?

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okpalawalter8 okpalawalter8 · Answer 1 · 2020-03-06T15:45:08+01:00

Complete Question

The complete question is shown on the first uploaded image

Answer:

FWOC should hire 70,000 hunters to completely remove the python in the area

Step-by-step explanation:

From the question we are given that the Initial Pythons [tex]P_o=[/tex] 100,000

And the final python [tex]P_f[/tex] [tex]=100,000+\frac{P}{10,000}(100,000-P)[/tex]

[tex]P_f = 100,000 + 10P -\frac{P^2}{10,000}[/tex]

For Max Number of Python

=> [tex]\frac{dP_f}{dP} = 0[/tex]

=> [tex]\frac{dP_f}{dP} =[/tex] [tex]100,000 -2P = 0[/tex]

=> [tex]P = 50,000[/tex]

Hence the maximum number of pythons [tex]Max_P[/tex] [tex]=100,000 +\frac{50,000}{10,000} (50,000)[/tex]

[tex]=350,000[/tex]

Using Mathematical relations

from the Question

5 python is killed by = 1 hunter

1 python is killed by = [tex]\frac{1}{5} \ hunters[/tex]

350 , 000 pythons are killed by = [tex]\frac{350,000}{5}[/tex]

[tex]= 70,000 \ hunters[/tex]